Abstract
We use identification robust tests to show that difference (Dif), level (Lev), and nonlinear (NL) moment conditions, as proposed by Arellano and Bond (1991, Review of Economic Studies 58, 277–297), Ahn and Schmidt (1995, Journal of Econometrics 68, 5–27), Arellano and Bover (1995, Journal of Econometrics 68, 29–51), and Blundell and Bond (1998, Journal of Econometrics 87, 115–143) for the linear dynamic panel data model, do not separately identify the autoregressive parameter when its true value is close to one and the variance of the initial observations is large. We prove that combinations of these moment conditions, however, do so when there are more than three time series observations. This identification then solely results from a set of, so-called, robust moment conditions. These robust moments are spanned by the combined Dif, Lev, and NL moment conditions and only depend on differenced data. We show that, when only the robust moments contain identifying information on the autoregressive parameter, the discriminatory power of the Kleibergen (2005, Econometrica 73, 1103–1124) Lagrange multiplier (KLM) test using the combined moments is identical to the largest rejection frequencies that can be obtained from solely using the robust moments. This shows that the KLM test implicitly uses the robust moments when only they contain information on the autoregressive parameter.
Highlights
It is common to estimate the parameters of linear dynamic panel data models using the generalized method of moments (GMM; Hansen, 1982)
Using power curves of the KLM test, we show that Dif, Lev, and NL moment conditions separately do not identify the autoregressive parameter for persistent values of it when paired with a large variance of the initial observations
Stylized Facts 1–4 illustrated by Figures 1–3 show the identification issues that occur for the autoregressive parameter θ when the variance of the initial observations is large and θ0, i.e., the true value in the data generating process (DGP), is close to one
Summary
It is common to estimate the parameters of linear dynamic panel data models using the generalized method of moments (GMM; Hansen, 1982). They are a subset of the moment conditions in Kruiniger (2002), which are derived under the additional assumption of time series homoskedasticity Despite these positive identification results for the Sys and AS moments, the large sample distributions of corresponding one-step and two-step GMM estimators are known to be nonstandard when the variance of the initial observation is large and the autoregressive parameter is close to one. It discusses identification robust statistics, the KLM test, that we use to illustrate the identification issues that occur at persistent values of the autoregressive parameter. Convergence in probability is denoted by “→”, convergence in p distribution by “→”, and “=” means asymptotically equivalent
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
